# A Study of Wall-Crossing: Flavored Kinks in D=2 QED

## TL;DR

This paper investigates the spectrum and wall-crossing phenomena of flavored BPS kinks in two-dimensional N=(2,2) QED, revealing new insights into their quantum degeneracies, spectrum correspondence with four-dimensional theories, and complex supermultiplet structures.

## Contribution

It provides a detailed analysis of flavored kink solitons in D=2 N=(2,2) QED, including their quantum degeneracies and a novel connection to D=4 Seiberg-Witten theory beyond hypermultiplets.

## Key findings

- Flavored kinks are more numerous and qualitatively different in the large mass regime.
- Spectrum correspondence extends beyond hypermultiplets to include complex dyon supermultiplets.
- Wall-crossing behavior of BPS states is characterized and compared to D=4 dyons.

## Abstract

We study spectrum of D=2 N=(2,2) QED with N+1 massive charged chiral multiplets, with care given to precise supermultiplet countings. In the infrared the theory flows to CP^N model with twisted masses, where we construct generic flavored kink solitons for the large mass regime, and study their quantum degeneracies. These kinks are qualitatively different and far more numerous than those of small mass regime, with features reminiscent of multi-pronged (p,q) string web, complete with the wall-crossing behavior. It has been also conjectured that spectrum of this theory is equivalent to the hypermultiplet spectrum of a certain D=4 Seiberg-Witten theory. We find that the correspondence actually extends beyond hypermultiplets in D=4, and that many of the relevant indices match. However, a D=2 BPS state is typically mapped to several different kind of dyons whose individual supermultiplets are rather complicated; the match of index comes about only after summing over indices of these different dyons. We note general wall-crossing behavior of flavored BPS kink states, and compare it to those of D=4 dyons.